test_bessel_j.cpp

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//  (C) Copyright John Maddock 2007.
//  Use, modification and distribution are subject to the
//  Boost Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/bessel.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "handle_test_result.hpp"
#include "test_bessel_hooks.hpp"

//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the bessel functions.  There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at 
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms.  In this situation you will 
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable.  Either way please
// report the results to the Boost mailing list.  Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//

void expected_results()
{
   //
   // Define the max and mean errors expected for
   // various compilers and platforms.
   //
   const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
   {
      largest_type = "(long\\s+)?double|real_concept";
   }
   else
   {
      largest_type = "long double|real_concept";
   }
#else
   largest_type = "(long\\s+)?double";
#endif
   //
   // HP-UX specific rates:
   //
   // Error rate for double precision are limited by the accuracy of
   // the approximations use, which bracket rather than preserve the root.
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "HP-UX",                          // platform
      largest_type,                      // test type(s)
      ".*J0.*Tricky.*",              // test data group
      ".*", 80000000000LL, 80000000000LL);         // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "HP-UX",                          // platform
      largest_type,                      // test type(s)
      ".*J1.*Tricky.*",              // test data group
      ".*", 3000000, 2000000);         // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "HP-UX",                          // platform
      "double",                      // test type(s)
      ".*Tricky.*",              // test data group
      ".*", 100000, 100000);         // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "HP-UX",                          // platform
      largest_type,                      // test type(s)
      ".*J.*Tricky.*",              // test data group
      ".*", 3000, 500);         // test function
   //
   // HP Tru64:
   //
   add_expected_result(
      ".*Tru64.*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "double",                      // test type(s)
      ".*Tricky.*",              // test data group
      ".*", 100000, 100000);         // test function
   add_expected_result(
      ".*Tru64.*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                      // test type(s)
      ".*Tricky large.*",              // test data group
      ".*", 3000, 1000);         // test function
   //
   // Solaris specific rates:
   //
   // Error rate for double precision are limited by the accuracy of
   // the approximations use, which bracket rather than preserve the root.
   //
   add_expected_result(
      ".*",                              // compiler
      ".*",                              // stdlib
      "Sun Solaris",                     // platform
      largest_type,                      // test type(s)
      "Bessel J: Random Data.*Tricky.*", // test data group
      ".*", 3000, 500);                  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Sun Solaris",                 // platform
      "double",                      // test type(s)
      ".*Tricky.*",                  // test data group
      ".*", 200000, 100000);         // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Sun Solaris",                 // platform
      largest_type,                  // test type(s)
      ".*J.*tricky.*",               // test data group
      ".*", 400000000, 200000000);    // test function
   //
   // Mac OS X:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                  // test type(s)
      ".*J0.*Tricky.*",              // test data group
      ".*", 400000000, 400000000);   // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                  // test type(s)
      ".*J1.*Tricky.*",              // test data group
      ".*", 3000000, 2000000);       // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                      // test type(s)
      "Bessel JN.*",              // test data group
      ".*", 40000, 20000);         // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                      // test type(s)
      "Bessel J:.*",              // test data group
      ".*", 50000, 20000);         // test function



   //
   // Linux specific results:
   //
   // sin and cos appear to have only double precision for large
   // arguments on some linux distros:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "linux",                          // platform
      largest_type,                      // test type(s)
      ".*J:.*",              // test data group
      ".*", 40000, 30000);         // test function


#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   if((std::numeric_limits<double>::digits != std::numeric_limits<long double>::digits)
      && (std::numeric_limits<long double>::digits < 90))
   {
      // some errors spill over into type double as well:
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "double",                      // test type(s)
         ".*J0.*Tricky.*",              // test data group
         ".*", 400000, 400000);         // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "double",                      // test type(s)
         ".*J1.*Tricky.*",              // test data group
         ".*", 5000, 5000);             // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "double",                      // test type(s)
         ".*(JN|j).*|.*Tricky.*",       // test data group
         ".*", 50, 50);                 // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "double",                      // test type(s)
         ".*",                          // test data group
         ".*", 30, 30);                 // test function
      //
      // and we have a few cases with higher limits as well:
      //
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         ".*J0.*Tricky.*",              // test data group
         ".*", 400000000, 400000000);   // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         ".*J1.*Tricky.*",              // test data group
         ".*", 5000000, 5000000);       // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         ".*(JN|j).*|.*Tricky.*",       // test data group
         ".*", 33000, 20000);               // test function
   }
#endif
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*J0.*Tricky.*",              // test data group
      ".*", 400000000, 400000000);   // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*J1.*Tricky.*",              // test data group
      ".*", 5000000, 5000000);       // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*JN.*Integer.*",              // test data group
      ".*", 30000, 10000);       // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*(JN|j).*|.*Tricky.*",       // test data group
      ".*", 1500, 700);               // test function
   add_expected_result(